PDE Seminar

DATE2023-05-17 14:10-15:00

PLACE數學系館 3F會議室

SPEAKERProf. Bastian von Harrach(Institute of Mathematics. Goethe University Frankfurt (德國法蘭克福大學數學研究所)

TITLEInverse Problems in Partial Differential Equations

ABSTRACT Several novel noninvasive imaging methods lead to the problem of determining the coefficient in a partial differential equation (PDE) from (partial) knowledge of its solutions. A prominent example is the emerging technique of electrical impedance tomography (EIT), where electrical currents are driven through a patient to image its interior, which leads to the famous mathematical Calder?n problem.
In our talk, we will describe recent mathematical advances on inverse problems for elliptic PDEs. Specifically, we show how to overcome the problem of non-linearity by using monotonicity relations and the concept of localized potentials. We also point out a new connection to semidefinite convex optimization that may yield to globally convergent reconstruction.